Implementation in mixed Nash equilibrium

• 成果类型: Article
• 署名作者: Mezzetti, Claudio; Renou, Ludovic
• 署名单位: University of Melbourne; University of Essex
• 刊物名称: JOURNAL OF ECONOMIC THEORY
• ISSN/ISSBN: 0022-0531
• DOI: 10.1016/j.jet.2012.09.004
• 发表日期: 2012
• 页码: 2357-2375
• 关键词: Implementation; Maskin monotonicity; Pure and mixed Nash equilibrium; Set-monotonicity; Social choice correspondence

摘要

A mechanism implements a social choice correspondence f in mixed Nash equilibrium if, at any preference profile, the set of all (pure and mixed) Nash equilibrium outcomes coincides with the set of f -optimal alternatives for all cardinal representations of the preference profile. Unlike Maskin's definition, our definition does not require each optimal alternative to be the outcome of a pure equilibrium. We show that set-monotonicity, a weakening of Maskin's monotonicity, is necessary for mixed Nash implementation. With at least three players, set-monotonicity and no-veto power are sufficient. Important correspondences that are not Maskin monotonic can be implemented in mixed Nash equilibrium. (c) 2012 Elsevier Inc. All rights reserved.